Mathematical Finance with MATLAB©

Authors

  • María Merino Departamento de Matemática Aplicada, Estadística e Investigación Operativa Universidad del País Vasco
  • Fernando Vadillo Departamento de Matemática Aplicada, Estadística e Investigación Operativa Universidad del País Vasco

DOI:

https://doi.org/10.46661/revmetodoscuanteconempresa.2067

Keywords:

MATLAB, Ibex 35, valoración de opciones, componentes principales, ecuaciones de Black-Scholes, método Monte Carlo, método binomial, options valuation, principal components, Black-Scholes equations, Monte Carlo method, binomial method

Abstract

The aim of this paper is to present the MATLAB tools for the teaching and the applications in the Mathematical Finance. This paper has two parts; the first one is a statistical study of the movement of the prices for the securities in the Ibex 35 during the year 2006. The second one is about the different procedures: the Black-Scholes equation, Monte-Carlo method and Binomial method, to calculate the prices of financial options.

Downloads

Download data is not yet available.

References

L. Bachelier, Theorie de la speculation, Annales de l’École Normale Superieure (1900), no. 17, 21–86.

F. Blach and M. Scholes, The Princing of Options and Corporate Liabilities, Journal of Political Economy (1973), no. 81, 637–59.

L. Boltzmann, Über die mechanische Bedeutung des Zweiten Haupsatzes der Wärmetheorie, Wien. Ber. (1866), no. 53, 195–220.

L. Boltzmann, Studien über das Gleichgewichtder lebendigen Kraft zwischen bewegten materiellen Punkten, Wien. Ber. (1868), no. 58, 517–560.

L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen, Wien. Ber. (1872), no. 66, 275–370.

R. Brown, A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies, Phil. Mag. (1828), no. 4, 161–173.

J.C. Cox, S.A. Ross, and M. Rubinstein, Option princing: a simplied approach, Journal of Financial Economics (1979), no. 7, 229–263.

B. del Hoyo and F. Vadillo, Sobre la enseñanza del Análisis Numérico, Boletin de la Sociedad Española de Matemática Aplicada (2005), no. 33, 13–18.

A. Einstein, Folgerungen aus den Capillaritätserscheinungen, Ann. Phys. (Leipzig) (1901), no. 4, 513–523.

B.S. Everitt, The Cambridge Dictionary of Stastistic, 3th edn, Cambridge Unersity Press, 2006.

P. Glasserman, Monte Carlo Methods in Financial Enginnering, Springer, 2004.

D.J. Higham, An Introduction to Financial Option Valuation, SIAM, 2000.

D.J. Higham and N.J. Higham, MATLAB Guide, SIAM, 2000.

D.J. Higham and P.E. Kloeden, Maple and Matlab for E.D.E. in Finance, disponible en: www.maths.strath.ac.uk.

H. Hotelling, Analysis of a complex of statistical variables into principal components, J. Educ. Psychol. (1933), no. 24, 417–441, 498–520.

H. Hotelling, Simplified calculation of principal components, Psychometrika (1936), no. 1, 27–35.

J. Hull, Introducción a los mercados de futuros y opciones, Prentice Hall, 1996.

J. Hull, Options, Futures and Others Derivatives, 4th edn, Prentice Hall, 2000.

E. Mach, Die Principien der Wärmelehre: Historisch-kritisch entwickelt, Leipzig, Johann Ambrosius Barth, 1896.

E. Mach, Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen, Physikalische Zeitschrift (1910), no. 11, 599–606.

J. C. Maxwell, On the Dynamical Theory of Gases, Philosophical Transactions (1866), no. CLVII, 49–88.

R.C. Merton, Theory of rational option pricing, Bell Journal of Economics an Mangement Science (1973), no. 4, 141–183.

N. Metropolis, The Beginning of the Monte Carlo Method, Los Alamos Science (1987), no. 15, 125–130.

N. Metropolis and S. Ulam, The Monte Carlo method, J. of the American Statistical Association (1949), no. 44, 335–341.

C.B. Moler, MATLAB- an interactive matrix laboratory, University of New Mexico, Mathematics Department, Report 369 (1979).

C.B. Moler, Numerical Computing with MATLAB, SIAM, 2004.

W. Ostwald, Vorlesungen über Naturphilosophie, Leipzig, Johann Ambrosius Barth, 1901.

K. Pearson, On lines and planes of closest fit to system of points in space, Philos. Mag. (1901), no. 2, 559–572.

S.R. Ross, An Introduction to Mathematicl Finance, Cambrige University Press, 1999.

R. Seydel, Tools for Computational Finance. Third Edition, Springer, 2006.

S. Ulam, R.D. Richtmyer, and J. von Neumann, Statistical methods in neutron diffusion, Los Alamos Scientific Laboratory report LAMS-551 (1947).

N. Wiener, The mean of a functional of arbitrary elements, Ann. of Math. (1920), no. 22, 66–72.

N. Wiener, The average of an analytical functional and the Brownian movement, Proc. Nat. Acad. Sci. USA (1921), no. 7, 294–298.

P. Wilmont, Introduction Quantitative Finance, John Wiley & Sons, 2001.

P. Wilmont, S. Howison, and J. Dewynne, The Mathematic of Financial Derivatives. Un Student Introduction, Cambridge Univesity Press, 1995.

Published

2016-11-04

How to Cite

Merino, M., & Vadillo, F. (2016). Mathematical Finance with MATLAB©. Journal of Quantitative Methods for Economics and Business Administration, 4, Páginas 35 a 55. https://doi.org/10.46661/revmetodoscuanteconempresa.2067

Issue

Section

Articles